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We introduce the notion of ratio monotonicity for polynomials with nonnegative coefficients, and we show that for n ≥ 6, the q-derangement numbers Dn(q) are strictly ratio monotone, except for the las...
We prove new l'Hopital rules for monotonicity valid on an arbitrary time scale. Both delta and nabla monotonic l'Hopital rules are obtained. As an example of application, we give some new upper and lo...
We study a certain monotonicity property of ratios of means, which we call a strong inequality. These strong inequalities were recently shown to be related to the so-called relative metric. We also us...
The author uses certain property of convex functions to prove Bernoulli's inequality and to obtain a simple proof of monotonicity of power means.
A New Proof of the Monotonicity Property of Power Means.
Based on a ``monotonicity'' analogue of the l'Hospital Rule, monotonicity properties of the relative error are established for a Padé approximation of Mills' ratio.
This paper continues a series of results begun by a l'Hospital type rule for monotonicity, which is used here to obtain refinements of the Eaton-Pinelis inequalities for sums of bounded independent ra...
In this article, we give the monotonicity and concavity properties of some functions involving the gamma function and some equivalence sequences to the sequence n! with exact equivalence constants...
Monotonicity and Convexity for the Gamma Function.
In the short note, four sequences originating from Nanson's inequality are introduced, their monotonicities and convexities are obtained, and Nanson's inequality is refined.

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